The Representational Model

One of the core assumptions of the dimensional overlap model is that different types of consistency influence mental processing in different ways. As a result, the different task ensembles in the dimensional overlap taxonomy each have different underlying representation and processing assumptions; however, when two tasks are of the same task type in the taxonomy, then the same representation and processing mechanisms generate the effect–regardless of the specific stimuli and responses that are involved in the task (more info: What is consistency?, Taxonomy of DO Ensembles).

Dimensional Overlap Representational Boxology

The basic representational assumptions of the dimensional overlap model were originally presented by Kornblum, S., Hasbroucq, T., & Osman, A., (1990).  The most recent version of that model was presented by  Kornblum & Lee (1995), where the above figure first appeared.

Processing occurs in two modules, separated by a cut-point:  the Stimulus Vector (SV).  These modules have additive effects.  The first module is the input, or stimulus encoding & identification module. The second is the response production module, which has two branches: 1. the upper branch, Automatic Response Identity & Verification; and 2. the lower branch, Response Identification.  These two branches come together in the response-execution area, which consists of response-execution, response-abort, response program-retrieval and response execution.

When a stimulus is first presented, the input module generates a stimulus vector (SV) which consists of all the attributes or features encoded by the stimulus identification module, including the relevant and the irrelevant stimulus attributes. The relevant stimulus attribute is identified in the vector by a tag.

Whether or not the stimulus set and the response set overlap, the relevant stimulus in the stimulus vector activates the response identification process, which identifies the response that was specified by the mapping, i.e. the correct response.

Response identification (lower branch of the response production module) may be performed in one of three ways: by use of the identity rule, by use of a different rule but a rule nevertheless, or by search.  By assumption (supported by much evidence) the identity rule is the fastest; search in the longest; and “other rules”, depending on their complexity,  is usually in between.

When a stimulus has more than one dimension that can be varied (e.g. the shape of a stimulus and its location in space), one or both stimuli may be correlated with the response.  If both stimuli are correlated, they are called redundant  in the sense that the response can be identified on the basis of either.  However, if only one stimulus is correlated (and it is usually r = 1), it is called the relevant stimulus, and the other the irrelevant stimulus (usually r = 0), in the sense that it cannot be used to identify the response at a better than chance level.  Yet, when the irrelevant stimulus overlaps with the response and is consistent with it, it produces results that are qualitatively similar to the mapping effect that would have been obtained had that stimulus been relevant; i.e. RT is faster than if it had been inconsistent.

This representational model can be used to describe the underlying cognitive processing mechanisms behind the effects of dimeansional overlap  in each of the tasks in the dimensional overlap taxonomy (more info: Taxonomy of DO Ensembles).

Type 1 Tasks

When there is no S-R overlap in an ensemble, the only process triggered by the stimulus presentation is response identification, which is activated by the relevant (so tagged) attribute.  In the absence of DO, response identification proceeds by search.  After the correct response has been identified, the appropriate motor program is retrieved, and the response is then executed.

Type 2 Tasks

The model postulates that if a stimulus is presented that comes from a stimulus set that overlaps with the response set (e.g. Type 2 ensemble), it automatically activates its corresponding element in the response set.  This process is represented by the upper branch of the response-production stage.

Before being activated, the correctness of the automatically activated response is verified If the automatically activated response and the correct response are one and the same, then the automatically activated response is said to be congruent, and is executed without further ado. If the two differ, the automatically activated response is said to be incongruent, and: a) is aborted, b) the program for the correct response is retrieved, and c) that response is then executed.  Note that by being executed immediately after having been verified as correct, in contrast to the incongruent response which has to be aborted first and then have the appropriate program retrieved, both of which take time, the time to execute the congruent response will be shorter than for the incongruent response.  Automatic activation is said to have had a facilitative effect in the congruent case, and an interfering effect in the incongruent case.

If he S-R ensemble has no dimensional overlap (Type1), the response has not been activated automatically so that execution requires neither aborting the response, nor retrieving a new program.  The time to execute that response (the neutral case) will, therefore, be faster the incongruent case, but longer than the congruent.  Thus, the model predicts that the fastest response will be for the congruent mapping, the slowest for the incongruent mapping, and the time for the neutral response will fall between the two.

Type 3 Tasks

When the irrelevant stimulus set and the response set overlap, presentation of the stimulus element triggers automatic response activation as well as the response identification process.  However, each is activated by a different feature in the stimulus vector:

a. automatic response activation will be triggered by the stimulus feature that represents a value on the irrelevant stimulus dimension that overlaps with the response;

b. the response identification process will be triggered by the tagged, relevant feature that does not overlap with the response, and will necessarily use search in identifying the correct response.

Type 4 Tasks

If the relevant and the irrelevant stimulus set overlap (e.g. Type 4), then the presentation of a stimulus element automatically activates two stimulus identification codes ( “i” and “j” ) as potential candidates for the relevant stimulus.  If the two codes or features do not differ, then it matters little which is tagged as “i” or “j”, and one of them is passed on to the response production stage  If the two codes do differ, than one of them is tagged as relevant before being passed on to the response production stage.  It is on the basis of the tagged attribute that the correct response is subsequently identified.

Type 5 Tasks

Because the Hedge and Marsh task, a type 5 task, exhibits both relevant S-R overlap and irrelevant S-R overlap, both of the mechanisms at work for relevant and irrelevant S-R consistency come into play in this task. Essentially, this is a combination of a Type 2 and Type 3 task (more info: The Hedge and Marsh task).

This representational model, however, cannot explain the highly-debated reverse-Simon effect (more info: Debate: Explaining the reverse-Simon effect).

Kornblum and Stevens (1997, November) were able to show that the computational dimensional overlap model could explain the reverse-Simon effect, while still preserving key assumptions of the represntational model, if the activation of the irrelevant stimulus is suppressed below zero for long reaction times. More recently, a large volume of experimental data, both behavioral and neurological, has supported this suppression-below-zero hypothesis (e.g. van den Wildenberg et al., 2010) (more info:  The Computational Model).

Type 7 Tasks

The SS x SR Task, a type 7 task, is a straight-forward factorial combination of S-S overlap and irrelevant S-R overlap. The processing in this task is therefore simply a combination of the processing mechanisms in Type 3 and Type 4 tasks. Moreover, because S-S and S-R effects arise during different processing stages, the model predicts that the effects will be additive and will not necessarily exhibit the same time-course characteristics. These assumptions were tested by Kornblum (1994) (more info: The SS x SR Task).

Type 8 Tasks

According to the dimensional overlap process model, the Stroop task, a type 8 task, should exhibit all three consistency effects: relevant S-R, irrelevant S-R, and S-S. In most variations of the Stroop task, these effects are confounded so that it is impossible to determine whether all three types of consistency really produce an effect on performance. Zhang and Kornblum (1998) used a four-choice Stroop task with both compatible and incompatible mapping instructions to verify this prediction of the dimensional overlap process model: all three types of dimensional overlap in the task produced independent consistency effects (more info: The Stroop task).



This qualitative version of the model has enabled us to make ordinal predictions about consistency effects in various tasks that have been experimentally verified in our own labs, as well as others. A number of experiments that have been performed that have tested the predictions of the dimensional overlap model (more info: The Experiments).

One of the drawbacks of this simple box-and-arrow process model is that it is only able to make ordinal predictions, i.e. predict which conditions should be faster than others. In order to make quantitative predictions about both reaction time and errors in compatibility tasks, the basic assumptions of the dimensional overlap model were implemented as a computational model (more info: The Computational Model).

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Stimulus codes form automatically

One of the assumptions shared by all coding models of reaction time is that mental codes for irrelevant stimuli are formed automatically, even though they are not necessary to carry out a task. Coding models explain consistency effects in terms of a match or a mismatch between this irrelevant stimulus code and one of the mental codes required to perform the task.

This kind of explanation is very general, because mental codes can be about anything. As a result, any kind of irrelevant stimulus can give rise to a consistency effect: letters, words, locations, colors, and so on.  What these models must specify is exactly when and how irrelevant stimulus codes influence the formation of one or more of the mental codes that are required to carry out a task.

Wallace (1971, 1972) first suggested that the S-R consistency effect in a Simon task appears because people automatically, involuntarily form a spatial code, even though the stimulus position is irrelevant. Eriksen and Eriksen (1974; see also Eriksen & Schultz, 1979) similarly suggested that flanker letters in a Flanker task are identified (forming their own letter codes) even though they are known to be irrelevant to the task. This view has been generalized since then to apply to any irrelevant stimulus characteristic, and is an assumption made by all coding models of consistency effects.

Irrelevant stimulus codes form automatically, and influence the formation of other mental codes.  Many coding models assume that mental codes form gradually, and that selective attention will eventually suppress the formation of the irrelevant stimulus code once it is identified as irrelevant. This mechanism of attention produces a rising-then-falling, or inverted U-shaped activation of the irrelevant stimulus code.

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Debate: Processing Stages or Continuous Activation

Do stimulus and response processing happen in stages? Or does information get continuously transmitted from stimulus-processing to response-processing over time?

This is an important question that models of performance heatedly disagree about. According to the continuous transfer view, any activation that accumulates for a stimulus code is immediately used as input to any associated response codes, which in turn has an immediate influence on response code activation.  According to the discrete transfer view, on the other hand, activation of a stimulus code must accumulate to some critical level, indicating that stimulus identification has been completed with some degree of certainty, before a signal is sent to the response selection process and activation of the response codes can accumulate.

Historically, popularity has swung back and forth between these alternatives.  Over thirty years ago, Sternberg (1969) proposed a method of interpreting reaction time data called the additive factors method (AFM). This framework assumes that information is transferred discretely between processes, and shows that given this assumption, if the effect of manipulating some factor A changes (i.e. becomes larger or smaller) as one manipulates another factor B, then these two manipulations must influence the same underlying process.  The logic of this method was very compelling, and was used with much success for interpreting empirical results (see Sanders, 1980, 1990; Sternberg, 1971); so, people were happy, for a while, to assume discrete information transfer.

A decade later, however, McClelland (1979) developed the Cascade model, in which information is transferred continuously from stimulus to response processes, and showed that this model could account for many of the same kinds of empirical data that AFM could account for, but also allowed for different inferences to be drawn about what processes are influenced by experimental manipulations.  Around the same time, a large number of other criticisms of AFM also arose, as well as new models favoring the assumption of continuous information transfer (e.g. Eriksen & Schulz, 1979; Taylor, 1976; Wickelgren, 1977).  The tide had turned toward continuous models.

Approximately a decade after that, Miller (1988) brought extensive criticism against this shift, saying sharply: “We consider the en masse abandonment of discrete models in favor of continuous ones to be wholely unjustified given the evidence currently available, and thus scientifically premature.”  He analyzed much of the empirical data that had been adduced in support for continuous models, and found that they could all be accounted for by models that did not assume continuous information transfer.  Most often, the empirical evidence spoke against models that consisted of only a single unitary stimulus identification process, but could easily be accounted for by models that assumed the formation of multiple parallel stimulus codes.  Miller shows that his Asynchronous Discrete Coding (ADC) model, in which multiple stimulus identification processes each give separate and independent discrete outputs to response processing, is able to account for much of the critical data (see also Miller 1982a, 1982b, 1983).

Increasingly sophisticated methods have been proposed to empirically test whether information transfer is discrete or continuous (Roberts & Sternberg, 1993), and increasingly complex models have been proposed that manipulate assumptions about different ways in which information transmission can be discrete, continuous, or varying from one to the other on a continuum (e.g. Liu, 1996; Miller, 1993).  No overall agreement, however, has been reached in this debate.

Finally, it should be noted that the terms “discrete” and “continuous” can be, and have been, used in other ways when talking about models of mental processes.  Miller (1988) distinguishes between three different ways in which a model can be “discrete” or “continuous”.  First, it may have discrete or continuous representation: mental representations may either vary freely across a continuum, or may be restricted to a limited number of mental codes.  Second, it may have discrete or continuous transformation: mental representations may vary continuously in the degree to which they are formed or activated, or may have only a limited number of states they can be in (e.g. formed or not, prepared or not).  Third, it may have discrete or continuous transfer of information, as has been discussed so far here.  Most of the empirical tests and theoretical debates have been focused on the question of information transmission, although there has been some work in trying to empirically establish whether the transformation of information within response selection is discrete or continuous (e.g. Meyer, Irwin, Osman, Kounios, 1988; Meyer, Yantis, Osman, & Smith, 1985).

Connectionist models of performance and consistency effects all have discrete representation (a finite number of units, representing discrete mental codes) and continuous transformation (continuous accumulation of activation within each unit);  However, although most of these models assume continuous information transfer (e.g. Barber & O’Leary, 1993; Cohen, Dunbar & McClelland, 1990; Cohen & Huston, 1994; Cohen, Servan-Schreiber, & McClelland, 1992; O’Leary & Barber, 1997; Phaf, van der Heijden, & Hudson, 1990; Servan-Schreiber, 1990; Zhang & Kornblum, 1998), at least one of these models explicitly assumes discrete transfer (Kornblum, et al., 1999), and another implies it (Zorzi and Umilta, 1995; this case will be discussed below).

This debate is important when evaluating computational implementations of generic dimensional overlap and response selection models.  The way a model implements the transfer of information could seriously impact the predictions that it makes, also influencing any comparison that is made between it and other models.

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The link from stimulus to response

In connectionist network models of reaction time, stimulus codes are transformed into response codes through links that are set up between stimulus and response units.  These connections are thought of as associative links between concepts, stored in memory.  There can be both long-term memory (LTM) associations, and short-term memory (STM) associations (Barber & O’Leary, 1997).

LTM associations form between two units from repeated exposure over an extended period of time, such as the link between the stimulus unit for a written word and the response unit for saying that word, or the link between a stimulus unit for a particular location and a response unit for acting towards that location (since we often respond toward stimuli in our environment).

STM associations are temporary links formed between stimulus and response units based on a particular task at hand.  For example, if you are told to press a left key when you see a blue stimulus and to press a right key when you see a green stimulus, then a STM association would form between the “blue” stimulus code and the “left” response code, and between the “green” stimulus code and the “right” response code.  In the language of connectionist network models, there would be a temporary link between the “blue” stimulus unit and the “left” response unit.  This means that activation in the “blue” stimulus unit would be used as input to the “left” response unit, causing activation in the “left” response unit to increase.

According to these models, both controlled (intentional, deliberate, conscious) and automatic (unintentional, reflexive, unconscious) translation of a stimulus code into a response code happens through the same mechanism: activation in a stimulus unit is transformed into output, passed along an associative link, and used as input to a response unit, causing that response unit to accumulate activation.  STM associations implement the controlled translation from stimulus to response that is determined by the specific instructions of the task at hand.  Because STM associations encode the instructions of the task, they always link a stimulus to the correct corresponding response.  LTM associations, on the other hand, are based on previous experience, rather than the task at hand.  As a result, STM associations have also been called “controlled lines,” while LTM associations have been called “automatic lines” (Kornblum et al., 1999).

It is easy to see how the combination of automatic and controlled lines can allow these models to account for the S-R consistency effect (regardless of whether one is implementing a dimensional overlap model or a response selection model, because the mechanism accounting for S-R consistency is the same in both).  Consider, for example,  how information processing might proceed in a typical Simon task: a blue stimulus appears on the left side, causing activation to accumulate in the blue relevant stimulus unit and the left irrelevant stimulus unit; if the instructions assign a left key-press to blue stimuli, then activation from the blue relevant stimulus is passed along a STM association to the left response unit; activation of the left irrelevant stimulus unit is passed along a LTM association to the left response unit; because the response unit is getting input from both stimulus units, it has a high input, and activation accumulates quickly, reaching the threshold for completion in a short amount of time.  On the other hand, if the blue stimulus had appeared on the right side, the right irrelevant stimulus unit would have activated the right response unit through the LTM association, and input to the (correct) left response unit would have been lower.  Lower input, of course, means activation accumulates more slowly, and the decision threshold is reached later.

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